This Manifold of Ours

In the late 1300s, to Medieval Europeans, Asia was still a far away and exciting place. When ‘Sir John Mandeville’ published his Traveler’s Tales in the 1370s, readers in Europe were excited to read about the distant worlds of Persia, India, and China. While unreliable, it was a beginning, bridging the gap between the works of Marco Polo a century earlier, and the day the world changed nearly a century later. When Christopher Columbus sailed across the Atlantic in 1492, he was heavily influenced by the works of Sir John Mandeville.

Through the 1300s up to today, we have all had traveler’s tales, works that blend fact and story, observation and romance. There has always been a New World, long after the discovery of America. In the 1500s, the New World was the world of the sky when the telescope first came into use. A century after that, Physics was the Terra Nova and Sir Isaac Newton was quite possibly the greatest scientific explorer to ever live. After that, the great frontier lay in chemistry and the sciences of electricity and magnetism. Finally, beginning in the 1800s, the next frontier lay in biology. Medicine finally began to come into its own as a science, germ theory was discovered, and the idea of a cell as the fundamental unit of life finally came into the annals of science.

The final frontiers of science are well known to us all – biotech, nanotechnology, quantum physics and aerospace. Medieval scholars could never have dreamed of the ease of today’s nonstop flights to India, nor could they of our science today. They would read our traveler’s tales and find them fascinating. And indeed, there have been many tales and many books that have changed the world forever. Newton’s Principia Mathematica, Einstein’s Theory of Relativity, Carl Sagan’s Cosmos or Stephen Hawking’s A Brief History of Time. They all served to introduce the reader to worlds unknown.

It is time for a new Traveler’s Tale. It is time to tell the stories of the shapes that make up our world. I have had the pleasure, through most of my life, to have enough leisure to think about science and mathematics, and these mathematical musings have led to exciting discoveries.

Shapes compose everything that we know, because all the stuff in the universe takes on some form or another. From the great galaxies to the smallest of viruses, each item in the universe – and what a great plethora of forms they take on – has a design. The uniqueness of the butterfly from the sunflower, the differences in form between the galaxy and the blood cell – are vital and important. There is a law and a rule for everything. There is a reason that things take the shapes they do.

So, come inside! Adventure awaits. Our tales take us from the farthest corners of the galaxy to the smallest cells. We shall indeed go far, and we shall discover a new world. And not just the world – we shall discover this great manifold of ours.